The population of a town in 2010 was 8,500 people. The population has decreased by 4.5% each year since.
1. Write an equation showing how to find the population of the town t years after 2010.
2. In what year will the population of the town equal 7,000 people? Show your calculations.
Thank you!
+4622 (a) 8,500-4.5%(t)
(b) 2010: 8,500
2011: 8117
2012: 7752
2013: 7403
2014: 7069
2015: 6751
Thus, it'll be \(\boxed{2015}\) , when the population will equal 7000.
Present population =PP
Future population =FP
FP = PP x [1 - 0.045]^t
7,000 = 8,500 x [0.955]^t divide both sides by 8,500
0.823529... = 0.955^t take the log of both sides
t =Log(0.823529) / Log(0.955)
t = 4.22 = ~ 4.25 years after 2010 when the population of the town will be about 7,000.
